MRCI-MCSCF

For complementary studies (MRCI//MCSCF) of the H-F-B-O potential energy surface, see Soto [60,61]. 

However, the energy surface for formation of the acetylene is much more complex. As a result of MRCI-MCSCF calculations with a 4-31G -h DZP basis set, two hydrogens migrate the first is a 1,3-shift to generate a propenylidene and the second is a vicinal hydrogen shift to establish the acetylene as is well known for vinylidenes (Scheme 4.3). Further, the pathway of Scheme 4.2 was found to be nearly 20 kcal/mol higher than the favored one ... 

It is particularly desirable to use MCSCF or MRCI if the HF wave function yield a poor qualitative description of the system. This can be determined by examining the weight of the HF reference determinant in a single-reference Cl calculation. If the HF determinant weight is less than about 0.9, then it is a poor description of the system, indicating the need for either a multiple-reference calculation or triple and quadruple excitations in a single-reference calculation. 

It is possible to construct a Cl wave function starting with an MCSCF calculation rather than starting with a HF wave function. This starting wave function is called the reference state. These calculations are called multi-reference conhguration interaction (MRCI) calculations. There are more Cl determinants in this type of calculation than in a conventional Cl. This type of calculation can be very costly in terms of computing resources, but can give an optimal amount of correlation for some problems. 

The notation for denoting this type of calculation is sometimes more specihc. For example, the acronym MCSCF+1+2 means that the calculation is a MRCI calculation with single and double Cl excitations out of an MCSCF reference space. Likewise, CASSCF+1+2 and GVB+1+2 calculations are possible. 

MRCI (multireference configuration interaction) a correlated ah initio method multiconfigurational self-consistent field (MCSCF) a correlated ah initio method... 

Figure 1. Energetic ordering of vinylcarbene conformers and electronic states according to the MRCI/DZP//MCSCF/4-31G computations of Yoshimine et al.47...

One way of achieving size-consistency for a dissociation process is to use an MCSCF wave function as the reference. Unfortunately, as noted above, there are as yet no general multireference perturbation theory or multireference coupled-cluster treatments that can be applied to such an MCSCF reference function. For rather few electrons, as we shall see, the MRCI approach performs acceptably. 

Full Cl, including its full MCSCF and MRCI variants, are size-consistent and variational. 

We consider a multireference Cl (MRCI) wave function calculated from a set of MCSCF orbitals. The Cl reference state is denoted by CI> at X0 and by CI(g)> at the displaced geometry X0 + g. In addition to the reorthonormalization part, the MRCI orbital connection contains the MCSCF orbital... 

The gradient Ww may be calculated using a procedure similar to that for MCSCF and MRCI wave functions, since H 1) is an operator of rank 2. The molecular gradient becomes... 

The average value of the Hamiltonian Hln] with respect to an MCSCF or MRCI wave function may be written as... 

The configuration part of the electronic gradient is for both MCSCF and MRCI wave functions... 

With this recipe we can construct a number of different types of MCSCF wave functions. With an empty RAS2 space we obtain SDT...-CI wave functions depending how many holes we allow in RAS 1 and how many electrons we allow in RAS 3. If we add a RAS2 space and allow up to two holes in RAS 1 and max two electron sin RAS3 we obtain what has traditionally been called the second order Cl wave function. Many other choices are possible. Since we have reduced the Cl space, we can use more active orbitals distributed over the three subspaces. Recent application have used more than 30 active orbitals. The RASSCF method has so far not be extensively used because there is no obvious way to treat dynamic correlation effects unless one can use the MRCI method. However, ongoing work attempts to extend the CASPT2 method (see below) to RASPT2, which may make the RASSCF method more useful in future applications (P.-A. Malmqvist, unpublished work). 

Incased by a tactor roughly equal to the number ot configurations included in the TvICSCK iarge-scale MRCI wave ftmcLiuiis (many configurations in the MCSCF) can... 

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